#383⋊C₃ #4633

order	192
isoclinism	isoclinic class of #126⋊C₃
automorphism	Aut(G) = C₂×#560⋊C₃ (order 384) · Inn(G) = #126⋊C₃ · Out(G) = C₂²
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

Fitting, Sylow	#383 ⋊ C₃
derived	C₄² ⋊ C₃×C₄

38 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 24

A minimal faithful permutation representation — 2 generators on 20 points:

(1,2,3,4)(6,14,15,10,7,17)(8,9,11)(12,13,16,20,18,19);(5,17,9,20)(6,14,13,7)(8,12,11,15)(10,19,18,16)

Polycyclic presentation:

2,3,2^5|a^2=c,d^2=fg,e^2=f,d^a=df,e^a=eg,d^b=e,e^b=deg,f^b=g,g^b=fg

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 192);